Solve r_{t}=2i-5j+k

$$r _ { t } = 2 i - 5 j + k$$

Solve for j

$$j=\frac{2i+k-r_{t}}{5}$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$2i-5j+k=r_{t}$$

Subtract 2i from both sides.

$$-5j+k=r_{t}-2i$$

Subtract k from both sides.

$$-5j=r_{t}-2i-k$$

The equation is in standard form.

$$-5j=r_{t}-k-2i$$

Divide both sides by -5.

$$\frac{-5j}{-5}=\frac{r_{t}-k-2i}{-5}$$

Dividing by -5 undoes the multiplication by -5.

$$j=\frac{r_{t}-k-2i}{-5}$$

Divide r_{t}-2i-k by -5.

$$j=\frac{k}{5}-\frac{r_{t}}{5}+\frac{2}{5}i$$

Solve for k

$$k=r_{t}+5j-2i$$

Solution Steps

Swap sides so that all variable terms are on the left hand side.

$$2i-5j+k=r_{t}$$

Subtract 2i from both sides.

$$-5j+k=r_{t}-2i$$

Add 5j to both sides.

$$k=r_{t}-2i+5j$$